Find the true wind from the wind you feel
Add the heading to get the direction the true wind comes from.
The example is Bowditch’s: a ship on course 240° at 18 knots with an apparent wind of 30 knots from 40° off the starboard bow. Angles are measured from the bow, 0 to 180°, on the side the wind comes from.
The apparent wind is the wind you feel on a moving boat; the true wind is the wind you would feel if the boat stopped. The boat’s own motion adds a wind from dead ahead at the boat’s speed, so the two differ whenever you are under way. In an example from The American Practical Navigator (Bowditch), a ship on course 240° at 18 knots measures an apparent wind of 30 knots from 40° off the starboard bow, and the true wind is about 20 knots from 315°. The calculator above finds the true wind from the apparent wind, or the apparent wind from the true wind, for any boat.
True wind speed = √(A² + B² − 2 × A × B × cos α) · True wind angle θ: tan θ = A × sin α ÷ (A × cos α − B), past 90° when A × cos α is less than B · True wind direction = heading + θ with the wind on the starboard side, heading − θ on the port side. A is the apparent wind speed, α its angle off the bow and B the boat speed.
Apparent Wind and True Wind
On a boat moving through still air, you feel a wind from dead ahead at the boat’s own speed: at 10 knots in a calm, the apparent wind is 10 knots from dead ahead. If a true wind of 15 knots blows from dead ahead, the apparent wind is 15 + 10 = 25 knots; turn around and run before it, and it drops to 15 − 10 = 5 knots from dead astern (Bowditch). At any other angle the two combine as vectors: the apparent wind is the vector sum of the true wind and the boat’s motion reversed. Wind vanes and anemometers on a moving boat measure the apparent wind, so the usual problem on board is to work back to the true wind.
How to Calculate True Wind: the Vector Method
The true wind is the apparent wind less the wind made by the boat’s motion. Splitting each wind into a part along the boat and a part across it turns this into plain arithmetic, with the angles measured from the bow:
- Across the boat: A × sin α, the part of the apparent wind from abeam, which the boat’s motion doesn’t change.
- Along the boat: A × cos α − B, the part from ahead, less the wind the boat makes.
- True wind: its speed is √(across² + along²), and its angle off the bow is the angle whose tangent is across ÷ along, on the same side as the apparent wind.
Bowditch’s first example works out this way: across = 30 × sin 40° = 19.3 knots and along = 30 × cos 40° − 18 = 5.0 knots, so the true wind is 19.9 knots, 75.5° off the starboard bow. Add that angle to the heading on the starboard side, or take it away on the port side: 240° + 75.5° = 315.5°, the direction the true wind comes from. Bowditch, plotting on a maneuvering board, gets 20 knots from 315°. In its second example, a ship on course 270° at 10 knots with an apparent wind of 30 knots from 10° off the port bow, the true wind is 20.2 knots, 14.9° off the port bow, from 255.1°; the manual’s table gives 15° off the port bow and 2.02 times the ship’s speed. Its Table 30 solves the same problem in units of the ship’s speed.
From True Wind to Apparent Wind
Going the other way, add the boat’s wind instead of taking it away: along = W × cos β + B and across = W × sin β, where W is the true wind speed and β its angle off the bow. The apparent wind for a true wind of 10 knots, by boat speed and true wind angle:
| True wind angle | Boat at 5 kn | Boat at 10 kn | Boat at 20 kn |
|---|---|---|---|
| 0° | 15.0 kn at 0° | 20.0 kn at 0° | 30.0 kn at 0° |
| 45° | 14.0 kn at 30° | 18.5 kn at 22° | 28.0 kn at 15° |
| 90° | 11.2 kn at 63° | 14.1 kn at 45° | 22.4 kn at 27° |
| 135° | 7.4 kn at 106° | 7.7 kn at 68° | 14.7 kn at 29° |
| 180° | 5.0 kn at 180° | calm | 10.0 kn at 0° |
With the true wind on or ahead of the beam, the apparent wind is always stronger than the true wind. Running before the wind, it is weaker as long as the boat goes slower than twice the wind speed: at 10 knots before a 10-knot wind there is no wind on deck, and at 20 knots you feel 10 knots from dead ahead.
Why the Apparent Wind Moves Forward
On a moving boat the true wind is always on the same side as the apparent wind and farther aft, and the faster the boat goes, the more the apparent wind draws ahead of the true wind (Bowditch). A boat sailing at 6 knots with an apparent wind of 15 knots from 35° off the bow has a true wind of 10.7 knots from 53.8° off the bow. At that true wind angle, the VMG Calculator works out how much of the boat’s speed is made good toward the wind. The sides of a boat, port and starboard, are explained in our guide Port vs Starboard.
Which Speed and Heading to Use
The true wind of weather observations is measured relative to the Earth, with its direction from true north and named for where the wind blows from. To compute it on a moving vessel, Smith, Bourassa and Sharp (1999) list the heading, the course and speed over the ground, and the wind measured on board. This calculator moves the boat the way it heads. With the speed over the ground from a GPS, the result is the true wind as long as the boat moves the way it points; a current or leeway that sets it sideways makes the course over the ground differ from the heading. With the speed through the water from a log, the result is an estimate of the wind relative to the water, which differs from the true wind where there is a current. Enter a true heading for a true direction, or a magnetic heading for a magnetic one. Wind speeds in knots convert with the Knots to km/h Converter and the Knots to MPH Converter.
Frequently Asked Questions
What is apparent wind?
The wind you feel on a moving boat. It combines the true wind with the wind made by the boat’s own motion, which blows from dead ahead at the boat’s speed. Wind vanes and anemometers on board measure the apparent wind.
What is true wind?
The wind relative to the Earth: the wind you would feel if the boat were not moving. Weather observations give the true wind, named for the direction it blows from.
How do you calculate true wind from apparent wind?
Split the apparent wind into a part across the boat, A × sin α, and a part from ahead, A × cos α, and take the boat speed away from the part from ahead. The true wind speed is the square root of the sum of the two parts squared, and its angle off the bow is the angle whose tangent is across ÷ along.
Is apparent wind stronger than true wind?
It is always stronger with the true wind on or ahead of the beam. Running before the wind, it is weaker as long as the boat goes slower than twice the wind speed. At 5 knots with a true wind of 10 knots from 45° off the bow, the apparent wind is 14.0 knots.
Why is the true wind aft of the apparent wind?
Your own motion adds a wind from dead ahead, which swings the wind you feel forward. The faster you go, the more the apparent wind draws ahead of the true wind.
Should I use speed over ground or speed through the water?
Speed over the ground gives the wind relative to the Earth, the wind of weather observations, when the boat moves the way it points. Speed through the water gives an estimate of the wind relative to the water, which differs where there is a current.
Sources
- NGA, The American Practical Navigator (Bowditch), Vol. I (2019), art. 4009, True and Apparent Wind: still air, the 25- and 5-knot examples, the vector sum, examples 1 and 2, the true wind on the same side as and aft of the apparent wind (read Oct 21, 2026).
- NGA, Bowditch, Vol. II (2019), Table 30, Direction and Speed of True Wind in Units of Ship’s Speed: apparent wind to true wind in units of the ship’s speed, the true wind on the same side as the apparent wind and from farther aft (read Oct 21, 2026).
- Shawn R. Smith, Mark A. Bourassa and Ryan J. Sharp, Establishing More Truth in True Winds, Journal of Atmospheric and Oceanic Technology 16 (1999): 939–952: the true wind referenced to the Earth and true north, the heading, course and speed over the ground it needs, the estimate relative to the water from the heading and the speed through the water (read Oct 21, 2026).